Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:06 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a Monte Carlo
  	simulation study for a two-level growth
  	model for a continuous outcome (three-
  	level analysis)
  MONTECARLO:
  	NAMES ARE y1-y4 x w;
  	NOBSERVATIONS = 1000;
  	NREPS = 500;
  	SEED = 58459;
  	CUTPOINTS = x (1) w (0);
  	MISSING = y1-y4;
  	NCSIZES = 3;
  	CSIZES = 40 (5) 50 (10) 20 (15);
  	WITHIN = x;
  	BETWEEN = w;
  MODEL POPULATION:
  	%WITHIN%
  	x@1;
  	iw sw | y1@0 y2@1 y3@2 y4@3;
  	y1-y4*.5;
  	iw ON x*1;
  	sw ON x*.25;
  	iw*1; sw*.2;
  	%BETWEEN%
  	w@1;
  	ib sb | y1@0 y2@1 y3@2 y4@3;
  	y1-y4@0;
  	ib ON w*.5;
  	sb ON w*.25;
  	[ib*1 sb*.5];
  	ib*.2; sb*.1;
  MODEL MISSING:
  	[y1-y4@-1];
  	y1 ON x*.4;
  	y2 ON x*.8;
  	y3 ON x*1.6;
  	y4 ON x*3.2;
  ANALYSIS:	TYPE IS TWOLEVEL;
  MODEL:
  	%WITHIN%
  	iw sw | y1@0 y2@1 y3@2 y4@3;
  	y1-y4*.5;
  	iw ON x*1;
  	sw ON x*.25;
  	iw*1; sw*.2;
  	%BETWEEN%
  	ib sb | y1@0 y2@1 y3@2 y4@3;
  	y1-y4@0;
  	ib ON w*.5;
  	sb ON w*.25;
  	[ib*1 sb*.5];
  	ib*.2; sb*.1;
  OUTPUT:	TECH9 NOCHISQUARE;



INPUT READING TERMINATED NORMALLY



this is an example of a Monte Carlo
simulation study for a two-level growth
model for a continuous outcome (three-
level analysis)

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of replications
    Requested                                                  500
    Completed                                                  500
Value of seed                                                58459

Number of dependent variables                                    4
Number of independent variables                                  2
Number of continuous latent variables                            4

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4

Observed independent variables
   X           W

Continuous latent variables
   IW          SW          IB          SB

Variables with special functions

  Within variables
   X

  Between variables
   W


Estimator                                                      MLR
Information matrix                                        OBSERVED
Maximum number of iterations                                   100
Convergence criterion                                    0.100D-05
Maximum number of EM iterations                                500
Convergence criteria for the EM algorithm
  Loglikelihood change                                   0.100D-02
  Relative loglikelihood change                          0.100D-05
  Derivative                                             0.100D-03
Minimum variance                                         0.100D-03
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03
Optimization algorithm                                         EMA


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Number of missing data patterns            15
     Cluster information

       Size (s)    Number of clusters of Size s

          5            40
         10            50
         15            20

     Average cluster size        9.091

     Estimated Intraclass Correlations for the Y Variables

                Intraclass              Intraclass              Intraclass
     Variable  Correlation   Variable  Correlation   Variable  Correlation

     Y1           0.192      Y2           0.221      Y3           0.304
     Y4           0.327


SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION


     MISSING DATA PATTERNS (x = not missing)

           1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
 Y1        x     x  x  x     x  x           x     x
 Y2        x  x     x  x     x     x  x  x
 Y3        x  x  x  x     x     x  x           x
 Y4        x           x  x     x  x  x           x  x
 X         x  x  x  x  x  x  x  x  x  x  x  x  x  x  x
 W         x  x  x  x  x  x  x  x  x  x  x  x  x  x  x


     MISSING DATA PATTERN FREQUENCIES

    Pattern   Frequency     Pattern   Frequency     Pattern   Frequency
          1         242           6          31          11          35
          2          46           7          75          12          26
          3          50           8          90          13          25
          4         117           9          95          14          31
          5          82          10          45          15          10


COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION

Minimum covariance coverage value   0.100


     PROPORTION OF DATA PRESENT


           Covariance Coverage
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             0.713
 Y2             0.516         0.737
 Y3             0.499         0.500         0.696
 Y4             0.445         0.464         0.458         0.626
 X              0.713         0.737         0.696         0.626         1.000
 W              0.713         0.737         0.696         0.626         1.000


           Covariance Coverage
              W
              ________
 W              1.000





MODEL FIT INFORMATION

Number of Free Parameters                       16

Loglikelihood

    H0 Value

        Mean                             -4424.440
        Std Dev                             55.422
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992        -4553.368      -4553.248
           0.980       0.986        -4538.260      -4529.117
           0.950       0.966        -4515.604      -4513.658
           0.900       0.898        -4495.469      -4496.800
           0.800       0.784        -4471.083      -4472.463
           0.700       0.678        -4453.503      -4457.876
           0.500       0.488        -4424.440      -4426.009
           0.300       0.310        -4395.377      -4391.965
           0.200       0.208        -4377.797      -4376.545
           0.100       0.114        -4353.411      -4351.576
           0.050       0.052        -4333.277      -4332.209
           0.020       0.018        -4310.620      -4311.383
           0.010       0.006        -4295.512      -4299.992

Information Criteria

    Akaike (AIC)

        Mean                              8880.880
        Std Dev                            110.844
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994         8623.024       8628.693
           0.980       0.982         8653.240       8653.822
           0.950       0.948         8698.553       8693.091
           0.900       0.886         8738.823       8734.600
           0.800       0.792         8787.594       8784.575
           0.700       0.690         8822.754       8815.366
           0.500       0.512         8880.880       8883.723
           0.300       0.322         8939.007       8946.980
           0.200       0.216         8974.167       8976.421
           0.100       0.102         9022.938       9023.993
           0.050       0.034         9063.208       9057.784
           0.020       0.014         9108.521       9087.750
           0.010       0.008         9138.737       9129.273

    Bayesian (BIC)

        Mean                              8959.404
        Std Dev                            110.844
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994         8701.548       8707.217
           0.980       0.982         8731.764       8732.346
           0.950       0.948         8777.077       8771.615
           0.900       0.886         8817.347       8813.124
           0.800       0.792         8866.118       8863.099
           0.700       0.690         8901.278       8893.890
           0.500       0.512         8959.404       8962.247
           0.300       0.322         9017.531       9025.505
           0.200       0.216         9052.691       9054.945
           0.100       0.102         9101.462       9102.517
           0.050       0.034         9141.732       9136.308
           0.020       0.014         9187.045       9166.274
           0.010       0.008         9217.261       9207.797

    Sample-Size Adjusted BIC (n* = (n + 2) / 24)

        Mean                              8908.587
        Std Dev                            110.844
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994         8650.731       8656.400
           0.980       0.982         8680.947       8681.529
           0.950       0.948         8726.260       8720.798
           0.900       0.886         8766.530       8762.307
           0.800       0.792         8815.301       8812.282
           0.700       0.690         8850.461       8843.073
           0.500       0.512         8908.587       8911.430
           0.300       0.322         8966.714       8974.688
           0.200       0.216         9001.874       9004.128
           0.100       0.102         9050.645       9051.701
           0.050       0.034         9090.915       9085.491
           0.020       0.014         9136.228       9115.457
           0.010       0.008         9166.444       9156.980



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff

Within Level

 IW       |
  Y1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 SW       |
  Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

 IW         ON
  X                   1.000     1.0012     0.1227     0.1192     0.0150 0.930 1.000

 SW         ON
  X                   0.250     0.2499     0.0846     0.0797     0.0071 0.938 0.856

 SW       WITH
  IW                  0.000     0.0019     0.0335     0.0334     0.0011 0.942 0.058

 Residual Variances
  Y1                  0.500     0.4967     0.0625     0.0645     0.0039 0.956 1.000
  Y2                  0.500     0.5001     0.0411     0.0401     0.0017 0.924 1.000
  Y3                  0.500     0.5025     0.0501     0.0479     0.0025 0.946 1.000
  Y4                  0.500     0.5003     0.0866     0.0863     0.0075 0.946 1.000
  IW                  1.000     0.9982     0.0852     0.0825     0.0072 0.938 1.000
  SW                  0.200     0.1992     0.0224     0.0215     0.0005 0.942 1.000

Between Level

 IB       |
  Y1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 SB       |
  Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

 IB         ON
  W                   0.500     0.5037     0.1215     0.1184     0.0147 0.936 0.988

 SB         ON
  W                   0.250     0.2488     0.0759     0.0737     0.0058 0.932 0.914

 SB       WITH
  IB                  0.000     0.0005     0.0241     0.0225     0.0006 0.938 0.062

 Intercepts
  Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  IB                  1.000     1.0002     0.0826     0.0851     0.0068 0.944 1.000
  SB                  0.500     0.5009     0.0516     0.0523     0.0027 0.944 1.000

 Residual Variances
  Y1                  0.000     0.0001     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  0.000     0.0001     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  0.000     0.0001     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  0.000     0.0001     0.0000     0.0000     0.0000 1.000 0.000
  IB                  0.200     0.1919     0.0507     0.0502     0.0026 0.934 0.996
  SB                  0.100     0.0973     0.0202     0.0196     0.0004 0.918 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.453E-02
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
                    0             0             0             0             0


           LAMBDA
              IW            SW            X
              ________      ________      ________
 Y1                 0             0             0
 Y2                 0             0             0
 Y3                 0             0             0
 Y4                 0             0             0
 X                  0             0             0


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1                 1
 Y2                 0             2
 Y3                 0             0             3
 Y4                 0             0             0             4
 X                  0             0             0             0             0


           ALPHA
              IW            SW            X
              ________      ________      ________
                    0             0             0


           BETA
              IW            SW            X
              ________      ________      ________
 IW                 0             0             5
 SW                 0             0             6
 X                  0             0             0


           PSI
              IW            SW            X
              ________      ________      ________
 IW                 7
 SW                 8             9
 X                  0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              Y1            Y2            Y3            Y4            W
              ________      ________      ________      ________      ________
                    0             0             0             0             0


           LAMBDA
              IB            SB            W
              ________      ________      ________
 Y1                 0             0             0
 Y2                 0             0             0
 Y3                 0             0             0
 Y4                 0             0             0
 W                  0             0             0


           THETA
              Y1            Y2            Y3            Y4            W
              ________      ________      ________      ________      ________
 Y1                 0
 Y2                 0             0
 Y3                 0             0             0
 Y4                 0             0             0             0
 W                  0             0             0             0             0


           ALPHA
              IB            SB            W
              ________      ________      ________
                   10            11             0


           BETA
              IB            SB            W
              ________      ________      ________
 IB                 0             0            12
 SB                 0             0            13
 W                  0             0             0


           PSI
              IB            SB            W
              ________      ________      ________
 IB                14
 SB                15            16
 W                  0             0             0


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           LAMBDA
              IW            SW            X
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 Y3             1.000         2.000         0.000
 Y4             1.000         3.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500
 Y4             0.000         0.000         0.000         0.500
 X              0.000         0.000         0.000         0.000         0.000


           ALPHA
              IW            SW            X
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              IW            SW            X
              ________      ________      ________
 IW             0.000         0.000         1.000
 SW             0.000         0.000         0.250
 X              0.000         0.000         0.000


           PSI
              IW            SW            X
              ________      ________      ________
 IW             1.000
 SW             0.000         0.200
 X              0.000         0.000         0.500


     STARTING VALUES FOR BETWEEN


           NU
              Y1            Y2            Y3            Y4            W
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           LAMBDA
              IB            SB            W
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 Y3             1.000         2.000         0.000
 Y4             1.000         3.000         0.000
 W              0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            W
              ________      ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 Y3             0.000         0.000         0.000
 Y4             0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           ALPHA
              IB            SB            W
              ________      ________      ________
                1.000         0.500         0.000


           BETA
              IB            SB            W
              ________      ________      ________
 IB             0.000         0.000         0.500
 SB             0.000         0.000         0.250
 W              0.000         0.000         0.000


           PSI
              IB            SB            W
              ________      ________      ________
 IB             0.200
 SB             0.000         0.100
 W              0.000         0.000         0.500


     POPULATION VALUES FOR WITHIN


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           LAMBDA
              IW            SW            X
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 Y3             1.000         2.000         0.000
 Y4             1.000         3.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500
 Y4             0.000         0.000         0.000         0.500
 X              0.000         0.000         0.000         0.000         0.000


           ALPHA
              IW            SW            X
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              IW            SW            X
              ________      ________      ________
 IW             0.000         0.000         1.000
 SW             0.000         0.000         0.250
 X              0.000         0.000         0.000


           PSI
              IW            SW            X
              ________      ________      ________
 IW             1.000
 SW             0.000         0.200
 X              0.000         0.000         1.000


     POPULATION VALUES FOR BETWEEN


           NU
              Y1            Y2            Y3            Y4            W
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           LAMBDA
              IB            SB            W
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         1.000         0.000
 Y3             1.000         2.000         0.000
 Y4             1.000         3.000         0.000
 W              0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            W
              ________      ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 Y3             0.000         0.000         0.000
 Y4             0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           ALPHA
              IB            SB            W
              ________      ________      ________
                1.000         0.500         0.000


           BETA
              IB            SB            W
              ________      ________      ________
 IB             0.000         0.000         0.500
 SB             0.000         0.000         0.250
 W              0.000         0.000         0.000


           PSI
              IB            SB            W
              ________      ________      ________
 IB             0.200
 SB             0.000         0.100
 W              0.000         0.000         1.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



     Beginning Time:  23:06:31
        Ending Time:  23:06:54
       Elapsed Time:  00:00:23



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